對於量子資訊而言，非古典光扮演了很重要的角色。為了實現利用量子資訊建
立的網絡，許多學者們正研究著單光子源和糾纏光子的物理性質。本篇論文主要
展示在自發四波混頻(spontaneous Four-Wave-Mixing ,sFWM)的機制下利用冷原
子產生時間-能量糾纏光子對(Time-energy entangle photon pairs)的理論以及
目前為止的實驗結果。我們利用銣87 產生的磁光陷阱(Magneto-optical
trap,MOT)進行實驗。
除了利用冷原子製備非古典光子對外，我們也嘗試利用DLCZ 架構進行量子
記憶(Quantum memory)的相關實驗，並簡單呈現到目前為止我們在實驗上的觀測
結果。

Non-classical light sources play a crucial role for quantum information process.
Therefore ,to realize the quantum information network, many people are working on studies of single photon source or quantum entanglement. In our experiments, we will demonstrate the mechanism of spontaneous Four-Wave-Mixing (sFWM) how we generate time-energy entangled photon pairs using cold atoms and show some results we have so far. We use Rubidium87 (Ru87) to produce Magneto-optical trap(MOT) as our atomic medium. Besides generating nonclassical photon pairs, we also tried to test the quantum memory experiment based on DLCZ protocol, and we’ll briefly mention our experimental observation up to present.

摘要 ................................................................................................................................. i
誌謝 ............................................................................................................................... iii
目錄 ............................................................................................................................... iv
第一章 緒論 .................................................................................................................. 1
第二章 自發四波混頻(spontaneous Four-Wave -Mixing)的理論計算 ............ 3
2.1 四波混頻的Interaction Hamiltonian ..................................................... 3
2.2 雙光子波形的頻域 ........................................................................................ 9
2.2.1 𝜅as(𝛥as)的頻域： ............................................................................. 9
2.2.2 𝛷as(𝛥as)的頻域： ........................................................................... 11
2.3 𝜅和𝛷對於雙光子波形的影響 .................................................................... 15
2.3.1 𝜅主導時的雙光子波形-------Damped oscillation region .... 17
2.3.2 𝛷主導時的雙光子波形------------Group delay region..... 20
2.3.3 EIT 對實驗的影響 ........................................................................... 22
第三章 實驗架設 .................................................................................................... 24
3.1 .尚未加入795nm 雷射前的實驗架設： .................................................... 24
3.2 795 波段雷射的架設 ................................................................................. 30
3.3 上桌版的實驗架設 ...................................................................................... 35
3.4 雙光子量測的時序設定 .............................................................................. 35
第四章 自發四波混頻的實驗結果 ........................................................................ 38
4.1 EIT 的量測 ................................................................................................... 38
4.2 雙光子訊號的量測結果 .............................................................................. 39
v
4.3 Coupling detuning 對於雙光子波形的影響 ........................................... 44
4.4 結論 .............................................................................................................. 48
第五章 DLCZ protocol 簡介及實驗 ..................................................................... 49
5.1 DLCZ protocol 簡介 .................................................................................. 49
5.2 DLCZ 實驗設定 ............................................................................................. 52
5.3 實驗結果 ...................................................................................................... 55
5.4 結論 .............................................................................................................. 60
第六章 總結 ................................................................................................................ 63
參考文獻 ...................................................................................................................... 64
附錄 .............................................................................................................................. 66

[1]Hui YanE and JieFei Chen, Narrowband polarization entangled paired photons with controllable temporal length, Science China Physics, Vol.58, Issue 7,pages1-10-Published April 17, 2015.

[2] Shengwang Du, Jianming Wen and Morton H. Rubin, Narrow-Band Biphoton Generation near Atomic Resonance, JOSA B, Vol. 25, Issue 12,pages C98-C108(2008).

[3] Shanchao Zhang, Ph.D. thesis, Coherent Quantum Interaction between Photons and Atoms, Department of Physics,The Hong Kong University of Science and Technology(2013).

[4] L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Long-distance quantum communication with atomic ensembles and linear optics, Nature Vol. 414, pages 413–418– Published 22 November 2001.

[5] 楊均偉，碩士論文，以冷原子群產生雙光子之理論與實驗架設，國立清華大學物理系(2017)

[6] 陳保鋼，碩士論文，銣87原子的二維磁光陷阱之設計及架設，國立清華大學物理系(2015)

[7] 謝宗樺，碩士論文，電磁引發透明：垂直相交之探測及耦合光束之研究，國立清華大學物理系(2017)

[8] Nicolas Sangouard, Christoph Simon, Hugues de Riedmatten, and Nicolas Gisin, Quantum repeaters based on atomic ensembles and linear optics, Rev. Mod. Phys. 83, 33 – Published 21 March 2011.

[9] Yu-Bo Sheng and Lan Zhou, Quantum Entanglement Concentration Based on Nonlinear Optics for Quantum Communications, Entropy, Volume 15, Number 5, pages 1776-1820–Published 16 May 2013.

[10] A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan and H. J. Kimble, Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles, Nature Vol. 423, pages 731–73412– June 2003

[11] Lucile Veissier, Ph.D. thesis, Quantum memory protocols in large cold atomic Ensembles, Quantum Physics [quant- ph]. Université Pierre et Marie Curie - Paris VI(2013).

[12] Rafael A. de Oliveira, Milrian S. Mendes, Weliton S. Martins, Pablo L. Saldanha, Jose ́ W. R. Tabosa and Daniel Felinto, Single-photon superradiance in cold atoms, Phys. Rev. A 90, 023848(2014).

[13] Wei-Mien Hsu, Yi-Hsin Chen, Jian-Siung Wang, and Ite A. Yu, Slow and stored light pulses in the presence of magnetic fields, Journal of the Optical Society of America B Vol. 30, Issue 8, pp. 2123-2129 (2013).